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Axiomatizing Rectangular Grids with no Extra Non-unary Relations
Fundamenta Informaticae ( IF 1.166 ) Pub Date : 2020-12-18 , DOI: 10.3233/fi-2020-1966
Eryk Kopczyński 1
Affiliation  

We construct a formula $\phi$ which axiomatizes non-narrow rectangular grids without using any binary relations other than the grid neighborship relations. As a corollary, we prove that a set $A \subseteq \mathbb{N}$ is a spectrum of a formula which has only planar models if numbers $n \in A$ can be recognized by a non-deterministic Turing machine (or a one-dimensional cellular automaton) in time $t(n)$ and space $s(n)$, where $t(n)s(n) \leq n$ and $t(n),s(n) = \Omega(\log(n))$.

中文翻译:

公理化没有额外非一元关系的矩形网格

我们构造了一个公式 $\phi$ ,它公理化非窄矩形网格,而不使用网格邻域关系以外的任何二元关系。作为推论,我们证明集合 $A \subseteq \mathbb{N}$ 是一个公式的频谱,如果数字 $n \in A$ 可以被非确定性图灵机识别(或一维元胞自动机)在时间 $t(n)$ 和空间 $s(n)$,其中 $t(n)s(n) \leq n$ 和 $t(n),s(n) = \Omega(\log(n))$。
更新日期:2020-12-18
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